U.S. patent number 9,276,480 [Application Number 14/140,008] was granted by the patent office on 2016-03-01 for optimal trajectory control for llc resonant converter for led pwm dimming.
This patent grant is currently assigned to Virginia Polytechnic Institute and State University. The grantee listed for this patent is Virginia Tech Intellectual Properties, Inc.. Invention is credited to Weiyi Feng, Shu Ji, Fred C. Lee.
United States Patent |
9,276,480 |
Feng , et al. |
March 1, 2016 |
Optimal trajectory control for LLC resonant converter for LED PWM
dimming
Abstract
Pulse width modulation is provided for controlling a resonant
power converter, particularly for dimming of light emitting diode
arrays without loss of efficiency. Dynamic oscillation due to the
beginning of a pulse width modulated pulse burst is limited by
shortening of the first and/or last pulse of a pulse bust such that
the first pulse of a subsequent pulse burst close to or to connect
with a full load steady-state voltage/current trajectory of the
power converter. Pulse shortening made be made substantially exact
to virtually eliminate dynamic oscillation but substantial
reduction in dynamic oscillation is provided if inexact or even
performed randomly.
Inventors: |
Feng; Weiyi (Blacksburg,
VA), Lee; Fred C. (Blacksburg, VA), Ji; Shu
(Blacksburg, VA) |
Applicant: |
Name |
City |
State |
Country |
Type |
Virginia Tech Intellectual Properties, Inc. |
Blacksburg |
VA |
US |
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Assignee: |
Virginia Polytechnic Institute and
State University (Blacksburg, VA)
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Family
ID: |
51728498 |
Appl.
No.: |
14/140,008 |
Filed: |
December 24, 2013 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20140312789 A1 |
Oct 23, 2014 |
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Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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61814943 |
Apr 23, 2013 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H02M
3/33507 (20130101); H05B 45/327 (20200101); H05B
45/39 (20200101); H05B 45/3725 (20200101); H05B
45/46 (20200101); H02M 3/33561 (20130101); H02M
1/0058 (20210501); H02M 3/337 (20130101); Y02B
70/10 (20130101) |
Current International
Class: |
H05B
37/00 (20060101); H05B 39/00 (20060101); H05B
41/00 (20060101); H02M 3/335 (20060101); H05B
33/08 (20060101); H02M 1/00 (20070101); H02M
3/337 (20060101) |
Field of
Search: |
;315/186 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Houston; Adam
Attorney, Agent or Firm: Whitham, Curtis, Christofferson
& Cook, P.C.
Parent Case Text
CROSS-REFERENCE TO RELATED APPLICATIONS
This application claims benefit of priority of U.S. Provisional
Application 61/814,943, filed Apr. 23, 2013, which is hereby
incorporated by reference in its entirety.
Claims
The invention claimed is:
1. A method of operating a resonant power converter, said method
comprising steps of generating a pulse waveform comprising pulses
at a first frequency for controlling generation of switching
signals to control application of input power to said power
converter, generating a pulse width modulated signal comprising
pulses of controllable duty cycle at a second frequency, and
periodically interrupting said pulse waveform in accordance with
said pulse width modulated signal wherein said first frequency is
sufficiently greater than said second frequency to form pulse
bursts from said pulse waveform, each said pulse burst comprising
at least three of said pulses.
2. The method as recited in claim 1, wherein said resonant power
converter is a LLC resonant power converter.
3. The method as recited in claim 2 wherein said power converter is
a multi-channel, constant current power converter.
4. The method as recited in claim 1, comprising a further step of
shortening at least one of a first pulse and a last pulse of a
pulse burst.
5. The method as recited in claim 4 wherein a first pulse is
shortened such that the voltage on a resonant capacitor due to said
first pulse of a subsequent pulse burst increases to correspond to
a full load, constant current voltage on said resonant
capacitor.
6. The method as recited in claim 4. wherein a last pulse is
shortened such that the voltage on a resonant capacitor is brought
to a voltage such that a first pulse of a subsequent pulse burst
increases voltage on said resonant capacitor to correspond to a
full load, constant current voltage on said resonant capacitor.
7. The method as recited in claim 1, wherein said step of
generating a pulse waveform is synchronized with said step of
generating a pulse width modulated signal such that bursts of
pulses having an integral number of pulses of equal pulse width are
produced.
8. The method as recited in claim 7, comprising a further step of
shortening at least one of a first pulse and a last pulse of a
pulse burst.
9. The method as recited in claim 8, wherein a first pulse is
shortened such that the voltage on a resonant capacitor due to said
first pulse of a subsequent pulse burst increases to correspond to
a full load, constant current voltage on said resonant
capacitor.
10. The method as recited in claim 8, wherein a last pulse is
shortened such that the voltage on a resonant capacitor is brought
to a voltage such that a first pulse of a subsequent pulse burst
increases voltage on said resonant capacitor to correspond to a
full load, constant current voltage on said resonant capacitor.
11. The method as recited in claim 1, wherein said step of
periodically interruption said pulse waveform with said pulse width
modulated signal shortens at least one of a first pulse and a last
pulse of a pulse burst.
12. The method as recited in claim 11, wherein said step of
generating a pulse waveform is synchronized with said step of
generating a pulse width modulated signal such that bursts of
pulses having an integral number of pulses with at least one of a
first pulse and a last pulse of a pulse burst is shortened such
that a first pulse of a subsequent pulse burst causes a
voltage/current state of the resonant power converter to coincide
with a full load steady-state voltage/current trajectory.
13. The method as recited in claim 11, wherein a first pulse is
shortened such that the voltage on a resonant capacitor due to said
first pulse of a subsequent pulse burst increases to correspond to
a full load, constant current voltage on said resonant
capacitor.
14. The method as recited in claim 11, wherein a last pulse is
shortened such that the voltage on a resonant capacitor is brought
to a voltage such that a first pulse of a subsequent pulse burst
increases voltage on said resonant capacitor to correspond to a
full load, constant current voltage on said resonant capacitor.
15. A resonant power converter comprising a switching circuit for
connecting and disconnecting a resonant circuit and a source of
power, a waveform generator for generating a pulse waveform to
control said switching circuit, and a pulse width modulator for
interrupting said pulse waveform to generate pulse bursts having at
least three pulses in each pulse burst.
16. A resonant power converter circuit as recited in claim 15,
further including means for shortening at least one of a first
pulse and a last pulse of a pulse burst.
17. A resonant power converter circuit as recited in claim 16,
wherein said means for shortening at least one of a first pulse and
a last pulse includes said pulse width modulator.
18. A resonant power converter circuit as recited in claim 15,
wherein said at least one of said first pulse and said last pulse
is shortened such that a first pulse of a subsequent pulse burst
charges a resonant capacitor to a voltage/current state that
coincides with a full load steady-state voltage/current trajectory
of said resonant power converter.
19. A light emitting diode array including a resonant power
converter wherein said resonant power converter comprises a
switching circuit for connecting and disconnecting a resonant
circuit and a source of power, a waveform generator for generating
a pulse waveform to control said switching circuit, and a pulse
width modulator for interrupting said pulse waveform to generate
pulse bursts having at least three pulses in each pulse burst.
20. A light emitting diode array as recited in claim 19, wherein
said resonant power converter is a LLC resonant power converter.
Description
FIELD OF THE INVENTION
The present invention generally relates to Illumination
arrangements using light-emitting diodes (LEDs) and, more
particularly, to operation of resonant power converters for
providing power to such illumination arrangements.
BACKGROUND OF THE INVENTION
Light-emitting diodes (LEDs) have been known for use in indicators
and selective electronic displays for many years. Many recent
advances in the technology of light-emitting diodes (LEDs) has
caused increased interest in using LEDs for purposes of
illumination and, indeed, made LED arrays the illumination medium
of choice for numerous applications such as exterior and interior
area illumination and backlighting of display panels due to the
efficiency, spectral content, long lifetime, eco-friendliness,
mechanical durability, safety and efficiency compared to
incandescent, fluorescent, mercury and sodium vapor and arc
lighting and the like.
Another important quality of LEDs for many such illumination
applications is the capability for full control of light output
flux, sometimes referred to as dimming. However, dimming of LEDs
presents some problems in the design of power supplies for LED
arrays particularly in providing good uniformity of light output of
all LEDs in an array and avoiding perceptible flickering consistent
with high efficiency of the power supply. For example, driving LEDs
individually or in long, series connected strings with individual
discrete power supplies is cost prohibitive and generally would
require complex cross-regulation to achieve acceptable uniformity
of light flux. Also, since power supplies are designed for highest
efficiency at a particular voltage and frequency, efficiency is
often greatly reduced as voltage is controlled, particularly when
that voltage control is achieved by frequency control in resonant
power converters. Moreover, Also, since light output flux of LEDs
terminates immediately upon interruption of current, duty cycle or
pulse width modulation (PWM) must be performed at a switching cycle
frequency above about 85 Hz whereas such a problem is not presented
by incandescent bulbs which exhibit a decrease in light output flux
over the period of filament cooling.
Among known designs of power converters, resonant switching power
converters have become popular due to their ability to limit
switching losses and electrical stresses during operation as well
as providing very high efficiency. Among resonant power converters,
so-called LLC resonant converters are becoming increasingly
attractive because of their flexibility of application, simplicity,
efficiency, the simplicity of their control the ability to deliver
a range of voltages and the possibility, although difficult, of
providing over-current protection.
Typically, an LLC resonant converter will comprise a pair of
switching transistors operated in a complementary fashion and a
resonant circuit comprising a capacitor and two inductors. An LLC
resonant converter typically operates at a switching frequency near
the resonant frequency, f.sub.0 of the LLC circuit for highest
efficiency. As an electrical load is increased and more power must
be delivered, simple sensing and feedback of the output voltage to
a voltage controlled oscillator (VCO) can be arranged to reduce the
switching frequency and increase the voltage gain to automatically
compensate for the increased required power and thus provide good
voltage regulation over a wide range of current. By the same token,
particular conditions of voltage, current or switching frequency
can be sensed and the VCO can be controlled to increase the
switching frequency to reduce gain of the power converter and thus
provide over-current protection in a very simple and robust manner.
However, while steady-state performance of resonant power
converters is well-matched to power requirements of LEDs other than
loss of efficiency due if switching frequency is used to control
voltage, interruption of input or output of power as is necessary
for PWM or duty cycle modulation (e.g. for dimming) causes
transients in the resonant circuit that may have perceptible
adverse effects on light output flux.
SUMMARY OF THE INVENTION
It is therefore an object of the present invention to provide a
unitary, resonant power supply capable of providing high uniformity
of light output flux of LEDs in an array and which is not
significantly susceptible to transients caused by use of PWM for
dimming.
It is another object of the invention to provide a switching
pattern control that substantially avoids transient effects in a
resonant power converter and thus permits use of PWM for dimming
consistent with use of a resonant power converter.
It is a further object of the invention to maintain efficiency of a
resonant power converter providing power to an LED array over a
full range of dimming ratio.
In order to accomplish these and other objects of the invention, a
method of operating a resonant power converter is provided
comprising steps of generating a pulse waveform comprising pulses
at a first frequency for controlling generation of switching
signals to control application of input power to the power
converter, generating a pulse width modulated signal comprising
pulses of controllable duty cycle at a second frequency, and
periodically interrupting the pulse waveform in accordance with
said pulse width modulated signal wherein the first frequency is
sufficiently greater than the second frequency to form pulse bursts
from the pulse waveform, each pulse burst comprising at least three
of said pulses.
In accordance with another aspect of the invention, a resonant
power converter is provided comprising a switching circuit for
connecting and disconnecting a resonant circuit and a source of
power, a waveform generator for generating a pulse waveform to
control the switching circuit, and a pulse width modulator for
interrupting the pulse waveform to generate pulse bursts having at
least three pulses in each pulse burst.
In accordance with a further aspect of the invention, a light
emitting diode array including a resonant power converter is
provided wherein said resonant power converter comprises a
switching circuit for connecting and disconnecting a resonant
circuit and a source of power, a waveform generator for generating
a pulse waveform to control the switching circuit, and a pulse
width modulator for interrupting the pulse waveform to generate
pulse bursts having at least three pulses in each pulse burst.
BRIEF DESCRIPTION OF THE DRAWINGS
The foregoing and other objects, aspects and advantages will be
better understood from the following detailed description of a
preferred embodiment of the invention with reference to the
drawings, in which:
FIG. 1 is a schematic diagram of a multi-channel constant current
(MC.sup.3) resonant LLC power converter for driving an LED
array,
FIG. 2 is a graph of loss of efficiency of the power converter of
FIG. 1 if switching frequency is used to control voltage,
FIG. 3 is a schematic diagram of an arrangement for controlling a
MC.sup.3 resonant power converter similar to that of FIG. 1 to
include PWM switching,
FIG. 3A is a table of parameters of the resonant power converter in
accordance with FIG. 3 used for experimental verification of the
efficacy of the invention for LED dimming,
FIG. 4 illustrates waveforms of a control scheme for the power
converter of FIG. 3 to provide pulse width modulated power to the
LED array,
FIGS. 5A and 5B respectively illustrate wave forms and a state
trajectory of dynamic oscillation that can occur in the power
converter of FIG. 4 when PWM is provided,
FIGS. 6A and 6B respectively illustrate wave forms and a state
trajectory of dynamic oscillation to avoid dynamic oscillation in
accordance with the invention by control of a first pulse of a PWM
pulse train in accordance with a first embodiment of the
invention,
FIG. 6C illustrates normalization of a portion of an elliptical
state trajectory for a technique of avoiding dynamic
oscillation,
FIGS. 6D and 6E illustrate waveforms and a state trajectory for a
change of resonant frequency of the resonant power converter after
avoidance of dynamic oscillation in accordance with FIGS.
6A-6C,
FIGS. 7A and 7B respectively illustrate wave forms and a state
trajectory of dynamic oscillation to avoid dynamic oscillation in
accordance with the invention by control of a last pulse of a PWM
pulse train in accordance with a second embodiment of the
invention,
FIG. 7C illustrates a graphical analysis for an alternative
technique for avoiding dynamic oscillation
FIGS. 7D and 7E illustrate waveforms and a state trajectory for a
change of resonant frequency of the resonant power converter after
avoidance of dynamic oscillation in accordance with FIGS.
6A-6C,
FIGS. 8 and 9 illustrate waveforms of LED PWM dimming for 50% and
2% dimming ratios, respectively,
FIGS. 10 and 11 illustrate a detailed comparison of waveforms of
LED PWM dimming with and without switching pattern control of the
invention,
FIGS. 12A and 12B illustrate experimental state trajectory
comparison with and without the switching pattern control of the
invention, and,
FIG. 12C illustrates a comparison of efficiency over a range of
dimming ratios with and without the switching pattern control of
the invention
DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT OF THE INVENTION
Referring now to the drawings, and more particularly to FIG. 1,
there is shown a schematic diagram of an exemplary resonant single
stage multi-channel constant current (MC.sup.3) power converter 10
useful for conveying an understanding the problems addressed by the
invention. Since this power supply arrangement is somewhat similar
in some aspects to some of the power supply arrangements disclosed
in U.S. patent application Ser. No. 13/114,181, filed May 24, 2011,
and a continuation-in-part thereof, U.S. patent application Ser.
No. 13/930,200, filed Jun. 28, 2013, both of which are hereby fully
incorporated by reference, no portion of FIG. 1 is admitted to be
prior art in regard to the present invention. Specifically, while
the power converter of FIG. 1 includes features of driving pairs of
LED strings (a pair of LED strings constituting two channels) using
voltage doubler circuits, series connection of transformer primary
windings to ensure equal currents to all voltage doublers and LED
strings, inclusion of DC blocking capacitors to ensure equal
voltages and currents to both LED strings of each pair and
control/cross-regulation of all strings of LEDs in accordance with
monitoring of a single channel or LED string using resistance Ri in
common with the power converters disclosed in the
above-incorporated U.S. Patent Applications which also disclose
numerous variations of such a power delivery arrangement which are
applicable to and suitable for the present invention, the power
converter topology is that of an LLC resonant power converter and a
controller 12 is interposed in the current monitoring feedback path
to achieve a variable dimming ratio. Use of the features in common
with the power converters disclosed in the above-incorporated
application allows variation in output light flux of LED strings in
the array to be held within a very small percentage of each other
even though the number of functional LEDs in each string may vary,
as disclosed therein.
Controller 12 includes a difference amplifier 14 used as a voltage
comparator to monitor the LED string current by comparing a voltage
developed across resistor Ri with a reference voltage V.sub.ref.
The voltage difference is coupled to voltage controlled oscillator
16 which generates and adjusts the frequency of control signals
V.sub.gsQ1 and V.sub.gsQ2 to control conduction of Q1 and Q2,
respectively. In general, the switching frequency, f.sub.s, will be
designed to be equal to or very slightly less than the resonant
frequency of the power converter under full load conditions.
However, when V.sub.ref is adjusted to control dimming, the
switching frequency is increased and the gain of the power
converter is reduced so that a lower voltage will be delivered to
the LED array; resulting in reduced current and a light load
condition is presented to the power converter under a low dimming
ratio (the ratio of dimmed light flux to maximum light flux).
A problem arises from the fact that, depending on the quality
factor of the resonant circuit, a relatively large frequency shift
is required to achieve a given reduction in voltage and resultant
dimming ratio. For example, a ten-fold increase in switching
frequency achieves only a 15% dimming ratio and efficiency drops
quickly, as shown in FIG. 2, as switching frequency is increased.
It should also be appreciated from the graph of FIG. 2 that extreme
switching frequencies are required to achieve dimming ratios below
15%.
Referring now to FIG. 3, a pulse width modulation (PWM) approach
300 to LED array dimming with a resonant converter similar to that
of FIG. 1 in accordance with the invention, is schematically
illustrated. Only four channels, each channel including an LED
string, are illustrated for simplicity. Otherwise, it may be
assumed that the resonant power converters are identical and that
as many channels as desired may be included. The only differences
in FIG. 3 from the arrangement of FIG. 1 are in the PWM dimming
circuit which can provide any arbitrarily low dimming ratio by
reduction of the width of control pulses that control the length of
pulse trains at an switching frequency close to the resonant
frequency of the resonant power converter. As depicted, however,
the current sensing resistor is illustrated as being in series with
the uppermost LED string. This last difference is solely for
clarity of illustration and is the electrical equivalent of the
location of Ri in FIG. 1 since the LED string (or channel) used for
current regulation is completely arbitrary. Since the switching
frequency is substantially maintained and the power converter is
operating at substantially full load during the arbitrarily short
periods when power is applied to the LED array, substantially full
operating efficiency is maintained regardless of the dimming ratio.
It should be understood that the depiction of functional elements
of the PWM LED dimming approach are arranged to convey an
understanding of the principles of the invention and that many
different circuits that will be evident to those skilled in the art
can be used depending on design requirements and manufacturing
economies.
The PWM approach to LED dimming begins with developing a PWM signal
which can be accomplished, for example, by a circuit 310 which
includes a comparator 320 receiving a control voltage V.sub.c and a
ramp voltage. The comparator 320 outputs a "1" signal voltage if
V.sub.c is greater than the ramp voltage and otherwise outputs a
"0" signal voltage. Therefore, the comparator 320 will output a
pulse train having a frequency which is the same as that of the
ramp signal (e.g. 200 Hz but any frequency above about 85 Hz, as
alluded to above, is suitable for avoiding flickering that is
perceptible to the human eye) and lower values of V.sub.c will
produce pulse of shorted duration and vice-versa.
Four switches S1-S4 are preferably used to control each respective
LED string. The PWM signal output of comparator 320 is used to
control S1-S4 to interrupt current in the respective LED strings
for periods when the output of comparator 320 is at a "0" value.
The same PWM signal is also input to digital controller 325 and
serves to gate the control signals for switches Q1 and Q2 as will
be discussed in greater detail below.
The magnitude information in the current sensing signal developed
on resistor Ri is preferably converted to a digital signal at
analog-to-digital converter (ADC) 330 and combined with (e.g.
subtracted from) a reference signal corresponding to full design
brightness of the array at logic element (or difference amplifier)
340 and the resulting signal provided to any closed loop
compensator (PI) 350 which provides a signal to control the
operating frequency of a digitally controlled oscillator (DCO) or
voltage controlled oscillator (VCO) 360 to make small adjustments
in switching signal frequency to slightly alter the gain of the
resonant power converter. The output of the VCO or DCO 360 is then
supplied to an AND gate or similar logic 370. Logic 370 also
receives the output of comparator 320 as an input and outputs
bursts of pulses having durations corresponding to the PWM dimming
signal. The VCO output is also provided to the PWM dimming circuit
310 to assure that the ramp waveform is synchronized therewith, as
illustrated at 380, such that an integral number of VCO output
pulses are supplied in each burst and that the initial and final
VCO pulses are not randomly foreshortened, as will be discussed in
greater detail below. In each burst, the pulse frequency will be
determined by the current feedback path and will thus be close to
the resonant frequency of the resonant power converter, as
illustrated by the waveforms of FIG. 4. Therefore, when a burst of
pulses is delivered to Q1 and Q2, power is delivered to the LED
strings and The LED strings will output light with full intensity
but when the pulse train is interrupted, power to the LED strings
will be interrupted and the LED strings will immediately become
dark. Thus, the apparent brightness of illumination will correspond
to the duty cycle of the PWM signal and any incremental degree of
dimming (e.g. to well below 1% of full brightness) can be achieved.
Moreover, any incremental arbitrary dimming ratio can be achieved
without significant alteration of the switching frequency of the
resonant power converter. (The term "incremental" is used since
dimming using PWM necessarily is a function of the number of pulses
in a PWM pulse burst and variation in brightness can be changed
step-wise and not continuously although the difference in frequency
between the nominal VCP frequency (e.g. about 120 KHz) and the PWM
dimming cycle frequency (e.g. about 200 Hz) is very large and the
incremental step-wise changes in brightness can be imperceptibly
small and approaches being continuously variable.) Since the
frequency of the PWM signal is far below the switching frequency of
the resonant power converter, a plurality of switching frequency
pulses in each PWM "on" period is also assured, even at very low
dimming ratios.
It should be appreciated that when the PWM signal passes a burst of
pulses to switches Q1 and Q2, the resonant power converter is being
controlled as if it were operating at full load in a steady state
mode of operation (although an actual steady state condition may
not be reached during the burst as will be discussed in greater
detail below) but when the pulses output by VCO 360 are interrupted
by logic 370, the resonant power converter is in an idle state and
no power is being delivered to the resonant circuit. Therefore, the
transition between an idle state and a full load state introduces
transients, as alluded to above, which, in turn, can cause dynamic
oscillation of the output of the resonant power converter which may
be perceptible to the human eye as reflected in the light output of
the LED strings.
A detailed mathematical analysis of the dynamic oscillations is set
out in "Optimal Trajectory Control of LLC Resonant Converters for
LED PWM Dimming" by W. Feng et al. which has been published
electronically by the IEEE Apr. 12, 2013 and is available from
their website and which is hereby fully incorporated by reference.
The article will be published in hard copy form in IEEE
Transactions on Power Electronics, Volume 29, Issue 2, February,
2014, pp. 979-987. However, the dynamic oscillations that can and
generally will be caused in the resonant power converter output can
be sufficiently understood for practice of the invention from FIGS.
5A and 5B. FIG. 5A illustrates waveforms of the PWM signal, the
control signals for Q1 and Q2 and the resulting waveforms of the
voltage, v.sub.Cr, on the resonant capacitor, and the currents in
the resonant inductor, i.sub.Lr, the magnetizing inductance,
i.sub.Lm, and the resulting current in the respective LED strings
(or switches S1-S4), i.sub.1,2,3,4. The variation in amplitude of
the peak and valley magnitudes of these currents and voltages is
readily apparent and the variation is a significant fraction of the
peak and valley values. It should be noted that the resonant
inductor waveform, i.sub.Lr is principally sinusoidal while the
current waveform of the magnetizing current, i.sub.Lm is
principally triangular and rises in average value following the
transition from an idle state to an active state as a steady state
is approached (but not necessarily reached due to termination of
the pulse train by the PWM signal). It should also be noted that
the peak and valley amplitude envelopes of the resonant inductor
current, i.sub.Lr, and resonant capacitor voltage, v.sub.Lr,
oscillate in approximate synchronism with each other.
FIG. 5B illustrates a so-called state trajectory representing these
waveforms. A state trajectory can best be visualized as a graph of
the current in the inductor(s) of a resonant circuit against the
voltage on the capacitor(s) of a resonant circuit. As is
well-understood in the art, when a resonant circuit is operated at
its resonant frequency, energy in the form of the voltage on one or
more capacitors or a current in one or more inductors is being
circulated between such inductors and capacitors. Such currents may
be plotted against such voltages and, when the resonant circuit is
operating at a steady state, will produce a closed geometric conic
section such as an ellipse. Since the plot reflects related changes
in voltage and current over a continuum of instants, the plot is
referred to as a trajectory in a state plane and a state
trajectory, although recently developed, has proven to be a useful
tool for analyzing steady state and transient behavior of resonant
circuits and resonant power converter circuits, in particular.
When such steady state voltage and current values are suitably
normalized in such a plot, the conic section will be a circle
having a radius, .rho., corresponding to the normalized peak
current and voltage since respective values are varying
sinusoidally with equal amplitude and a phase difference of
90.degree.. The circle will be centered at one-half of the input
voltage. Such a plot can easily be developed (or visualized) as a
Lissajous pattern on an oscilloscope.
Conversely, when a dynamic oscillation of amplitude of these
signals is present, the oscillation will appear as a distortion of
the circle (which may or may not be evident) and the amplitudes of
these signals will be transiently varying (causing a change in
diameter of the trajectory). Transients will appear as
discontinuities in the circles of differing diameters and changes
in amplitude will result in a spiraling shape of the trajectory;
all of which features are represented in the state trajectory of
dynamic oscillation in FIG. 5B. The distortions at the switching
instants t.sub.0, t.sub.2 (the turn on instant of Q1) and t.sub.1
(the turn on instant of Q2) are shown at 52 and 54,
respectively.
It should be noted that, at the switching points, the resonant
current is non-zero and the resonant capacitor voltage is slightly
less than the maximum resonant capacitor voltage. To achieve zero
voltage switching (ZVS), as is desirable, there should be current
in the resonant tank circuit to charge and discharge the junction
capacitances of the switches at the switching instant. It should
also be noted that, as will be discussed in greater detail below,
at the first turn-on time of Q1, L.sub.m participates in the
resonance and causes an ellipse trajectory which, without optimal
control in accordance with the invention, causes the corresponding
elliptical trajectory to cross the steady state circle and cause
oscillations. During these oscillations, the voltage/current
trajectories are not exact half circles as illustrated by brackets
at 52 and 54.
In the switching pattern using PWM, a conductive period of Q1 is
provided before the first conductive period of Q2 and after the
last conductive period of Q2 in a given PWM pulse burst. in order
to minimize switching losses at the instant the pulse burst begins
and the resonant power converter is placed into an active state
from an idle state since the voltage when Q1 is turned off
maintains the resonant capacitor voltage close to and within the
trajectory of the steady state circle and thus reduces voltage when
is again turned on at the first pulse of the next pulse burst.
However, the transition between these operational states causes a
serious dynamic oscillation in the resonant current which, in turn,
increases conduction losses while the oscillation in resonant
inductor current will reduce control accuracy of LED intensity.
In FIG. 5B, the full load steady-state trajectory is represented by
the innermost circular trajectory and is so labeled. When Q1 is
first turned on and power supplied to the converter, the secondary
sides of the multi-channel power supply will not conduct due to the
inductance in the circuit and the magnetizing inductance will
participate in the resonance. The state trajectory for the resonant
circuit including the magnetizing inductance will thus follow a
portion of an ellipse labeled as the first pulse trajectory fully
indicated by a dotted line. This portion of the elliptical
trajectory begins when Q1 is turned on and is terminated when Q1 is
turned off and determine the voltage on the resonant capacitor when
Q2 is turned on and thus determines the starting point of the state
trajectory that will be followed thereafter. The proximity of the
termination of the first pulse trajectory and the switching point
t.sub.1 (54) can be observed in FIG. 5B. Therefore, this portion of
the first pulse elliptical trajectory crosses the full load, steady
state trajectory, causing increased peaks 58 in the resonant
capacitor voltage which results in increased resonant currents and
dynamic oscillation as the larger diameter trajectories diminish
toward the steady state trajectory. It should be noted that
conduction losses diminish resonant voltages and currents and tend
to provide some degree of damping as reflected in spiral features
of the trajectory, while changes in input and output current toward
steady-state values of the resonant power converter can only occur
at the switching instants 52, 54.
The inventors have discovered that this behavior of the resonant
power converter in response to a change from idle to active state
can be minimized and substantially avoided by altering the duration
of the first pulse of the PWM-defined pulse train, which is also
the first conductive period of Q1, such that the first pulse
trajectory terminates substantially at (and does not significantly
cross) the full load steady-state trajectory. To understand this
methodology, it should be observed that since the conductive
periods of Q1 are provided prior and subsequent to conductive
periods of Q2 and conduction through the resonant power converter
is prevented between PWM pulse trains or bursts, the state
trajectory during the dimming off-period of the PWM signal will
correspond to zero current and a resonant capacitor voltage near
the full load steady-state circle. Therefore, by shortening the
duration of the first pulse, the PWM resonant converter can be
tuned to track the steady state circle very quickly; substantially
eliminating dynamic oscillation, as shown in FIGS. 6A and 6B. That
is, by shortening the initial conductive period of Q1 (e.g. at the
leading edge of the initial Q1 pulse) such that the voltage at the
end of the period substantially coincides with the steady state
trajectory, the steady state trajectory will be tracked almost
immediately when Q1 is turned off and Q2 becomes conductive.
The duration of the first pulse can be estimated from an analysis
of the state trajectory as will now be explained with reference to
FIG. 6A. As alluded to above, when a given on-time ends in a given
PWM dimming cycle, the voltage on the resonant capacitor will be
equal to the full load, steady state voltage when Q1 is turned off
(but Q2 is not turned on). That is (with the subscript N indicating
a normalized value),
v.sub.CrN(t.sub.n)=.pi.I.sub.full/n1/V.sub.in/Z.sub.0+0.5 In other
words, when the pulse train is interrupted by the turn-off of Q1
without turning on Q2 and assuming that full load steady state
operation has been at least approached, the trajectory shifts
vertically to a zero current location that will be slightly inside
the full load, steady state circle. Because both Q1 and Q2 are
non-conductive are turned off during the off part of the dimming
cycle, the circuit is lossless and the resonant capacitor voltage,
v.sub.Cr, remains constant. Then, when the next pulse burst begins
with the turn-on of Q1, the resonant capacitor voltage will be the
same to start the portion of the elliptical trajectory discussed
above.
From that trajectory starting point, the distance along the
elliptical trajectory to a desired connection point on the full
load, steady-state trajectory is very much shorter than the Q1
first pulse trajectory of FIG. 5, discussed above, and, in
accordance with the invention, Q1 is turned off and Q2 is turned on
after a very short period. The short duration of the optimized Q1
first pulse trajectory may be estimated by normalizing the voltages
and currents represented by the elliptical trajectory with
V.sub.in/Z.sub.1 where Z.sub.1=((L.sub.r+L.sub.m)/C.sub.r).sup.1/2
so that it becomes a circular trajectory and determining the angle,
.alpha., subtended by the arc of the circle defined by the points
A', B' corresponding to the optimized trajectory from point a to
point B along the ellipse, as shown in FIG. 6C. As alluded to
above, the closed state trajectories depict cyclical variations of
voltage and current that will occur and recur at a given frequency,
f, which also corresponds to an angular frequency, .omega..
Therefore, the distance along a circular arc, .omega..sub.1 of a
portion of a trajectory subtending angle .alpha. corresponds to a
time interval. Thus the conduction angle of Q1, .alpha.=cos.sup.-1
((1-v.sub.CrN(A')/(1-v.sub.CrN(B') can be converted into a time
domain conduction time, T, of Q1, as
T=.alpha./.omega..sub.1=.alpha./((L.sub.r+L.sub.m)/C.sub.r).sup.1/2
where .omega..sub.1 is the resonant frequency of (L.sub.r+L.sub.m)
with C.sub.r. Therefore, by tuning the first pulse to have
duration, T, the first pulse trajectory can be connected with a
trajectory that will be (when Q1 is turned off and Q2 is turned on)
the same current and voltage of the full load steady state
trajectory and dynamic oscillation can be eliminated. This tuning
can be accomplished in many ways that will be apparent to those
skilled in the art such as simple delay of the leading edge of the
first pulse with an RC circuit and logic gate that is disabled
after a first pulse with a so-called one shot multivibrator.
Alternatively, as may be preferred, the synchronization of VCO 360
and the PWM dimming circuit 310 can be shifted in phase to shorten
the initial pulse while leaving other pulses for controlling Q1 and
Q2 intact and suppressing any partial terminal Q2 pulse, as can be
achieved with simple logic in a gate array. Another possible
technique for digital application would be to program numbers of
pulses for Q1 and Q2 for each dimming ratio in a field programmable
gate array (FPGA) digital signal processor (DSP) or the like,
implement the PWM control with a pulse counter and simply delay the
leading edge of the initial Q1 pulse with and RC circuit and a
logic gate.
It has been found, however, that high accuracy in implementing the
estimation for optimizing the first pulse duration is not necessary
and that the optimum duration may change during operation and/or
over time due to shifting of the resonant frequency caused by
ambient temperature and/or aging of the inductors and capacitors.
FIGS. 6D and 6E illustrate the waveforms and state trajectory for
first pulse widths being 20% longer or shorter than the optimum for
a given resonant frequency, respectively. These waveforms and state
trajectories are valid to represent a similar shift of resonant
frequency and a fixed first pulse duration. It is readily seen that
dynamic oscillation remains very much reduced compared with FIG. 5
and that steady state conditions are reached much more rapidly.
The inventors have also found that similar avoidance or reduction
of dynamic oscillation can be achieved by tuning the last (Q1)
pulse of a PWM pulse burst. Waveforms and a state trajectory
representing a shortening of the last pulse of a PWM pulse burst
are illustrated in FIGS. 7A and 7B. When the last pulse (with Q1
conductive) in a PWM pulse burst is terminated at an earlier time
the state trajectory becomes substantially vertical as current is
rapidly reduced to zero as described above when the last pulse of a
burst is terminated normally at switching point 54 (FIG. 5).
However, the instantaneous voltage is much lower and the current
will be much higher; accounting for the significant apparent slope
(actually along a portion along a circular trajectory of large
radius since the resonant current is conducted by the body diode of
Q2) as the current diminishes. Therefore, a voltage closer to the
center of the circular full load steady-state trajectory as
determined by the reduced width of the tuned last pulse. As before,
this voltage is maintained constant through the period that the
resonant power converter is in an idle state. When the next pulse
burst begins, the magnetizing inductance will be included in the
resonance as before since all conditions are the same except the
resonant capacitor voltage and charge state and the state
trajectory will follow an elliptical trajectory as before but with
the trajectory shifted to begin at a lower voltage. Since, in this
case, the first pulse width is unchanged at one-half the
switching/resonant frequency (e.g. T.sub.0/2), the conduction
angle, .alpha., in the state plane normalized to transform the
elliptical trajectory to a circle can be determined as
.alpha.=T.sub.0/2.omega..sub.1=.pi.(L.sub.r+L.sub.m)). Thus, the
coordinate point in the transformed state plane corresponding to
point B' of FIG. 6A is v.sub.CrN(B')=1-(1-v.sub.CrN(A'))cos .alpha.
i.sub.CrN(B')=(1-.sub.CrN(A') sin .alpha. where N represents the
normalizing factor as above. Converting the normalizing factor to
V.sub.in/Z.sub.0, the normalized resonant current at point B of
FIG. 7C is i.sub.CrN(B)=1-(1-.sub.CrN(A)cos .alpha.Z.sub.0/Z.sub.1
which means that after a first pulse of T.sub.0/2 duration, the
elliptical trajectory beginning at point A will intersect with the
full load, steady state circle trajectory and the switching time to
place the voltage at point A can be found by solving the
right-triangle equation:
(v.sub.CrN(B)-0.5).sup.2((i.sub.LrN(A).sup.2=.rho..sup.2 to find
the time or voltage at which the last pulse should be terminated to
eliminate dynamic oscillation. Once the time or voltage at which
the final Q1 pulse should be terminated, that termination can be
implemented by phase shift of the VCO/PWM dimming circuit with
suppression of a leading Q1 pulse, if needed, or use of a digital
signal; processor (DSP) or counter and FPGA as discussed above.
FIGS. 7D and 7E show waveforms and state trajectory for the cases
where the voltage at point A is 20% larger and smaller than the
estimate, respectively, for optimizing the last pulse of a pulse
burst. Dynamic oscillation is larger than for the embodiment
optimizing the first pulse of a pulse burst but still settles to
the full load, steady state trajectory more quickly than when no
last pulse optimization is performed. This reduced degree of
dynamic oscillation is unlikely to be perceptible but represents a
divergent of LED string brightness from proportionality to the duty
cycle of the PWM. On the other hand, dynamic determination of the
termination point of the last pulse may be more easily performed by
a compensation circuit than for the case of first pulse
optimization and compensation for temperature and aging of
components of the resonant circuit may be accomplished
automatically.
It should be appreciated that the above analyses and design
methodologies for first pulse and last pulse optimization could be
used together, as might be advantageous in some applications, to
place the PWM off-time resonant capacitor voltage where it can
rapidly and accurately reach the full load steady state trajectory.
However, since either type of optimization can virtually eliminate
dynamic oscillation, using both techniques is considered to be an
unnecessary complication in view of the relatively slight
improvement in performance that might be available by doing so.
On the other hand, it should also be appreciated From FIGS. 5D-5E
and 7D-7E and the above discussion thereof that as long as no Q2
pulse precedes the initial Q1 pulse or follows the last Q1 pulse in
a burst, any shortening of the first or last Q1 pulse in a burst
will reduce voltage difference between the voltage state at the end
of the pulse burst and the full load, steady state trajectory and
thus reduce the magnitude and duration of dynamic oscillation
caused by PWM dimming control using a resonant power converter and
the tuning of the first and last pulses of a burst of switching
pulses can be considered as a perfecting features of the invention
not necessary to its successful practice in accordance with its
most basic principles. That is, if the first and last pulses in a
PWM VCO pulse burst are Q1 pulses, even a random shortening of
either or both of those pulses will reduce dynamic oscillation to
some finite degree although the magnitude and duration of the
dynamic oscillation will not be predictable or controllable without
synchronization 380 as discussed above. However, if such randomly
reduced dynamic oscillation is tolerable, synchronization 380 need
be no more than assuring that a Q2 control signal does not appear
as a first or last pulse in a PWM burst by appropriate timing or
logic.
The efficacy of pulse optimization in PWM dimming of LEDs has been
experimentally verified using a 200 W two channel MC.sup.3 LLC
resonant LED driver/power converter as depicted in FIG. 3 having
parameters as shown in Table 1 of FIG. 3A. FIGS. 8 and 9 show the
experimental waveforms when the dimming ratio is 50% and 2%,
respectively. At any dimming ratio, the LLC power converter
operates at full load during the PWM on-time. FIG. 10 shows the
detail waveforms using the optimized switching pattern and, for
comparison, FIG. 11 shows corresponding waveforms without
optimization of the switching pattern. Similarly, FIGS. 12A and 13
show the experimentally derive state trajectories of the waveforms
of FIGS. 10 and 11, respectively. All of these experimental results
agree well with the analysis and methodology described above.
Finally, FIG. 12C illustrates the gain in efficiency using PWM
modulation for LED dimming using a resonant power converter in
accordance with the invention over analog control of LED dimming
described above in connection with FIGS. 1 and 2. Note that
efficiency is maintained at above 94.6% down to a dimming ratio of
1%.
In view of the foregoing, it is seen that the invention provides
for maintaining efficiency of operation for LED dimming using a
resonant power converter over a greater range of dimming ratio than
is practical with analog dimming control using a resonant
converter. Optimization of the first pulse and/or the last pulse
avoids or reduces dynamic oscillation that, whether or not
perceptible variation in illumination is caused, avoids or reduces
variation from proportionality of LED illumination intensity and
the PWM duty cycle. Very high efficiency of the resonant power
converter is maintained over all dimming ratios from full
illumination to a dimming ratio of below 1%.
While the invention has been described in terms of a single
preferred embodiment, those skilled in the art will recognize that
the invention can be practiced with modification within the spirit
and scope of the appended claims.
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